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    Re: Long-range airplane navigation
    From: Ken Gebhart
    Date: 2004 Dec 1, 22:34 -0600

    on 11/29/04 11:55 AM, Cliff Sojourner at cls@EMPLOYEES.ORG wrote:
    > Ken, I for one would like to hear more about this.  could you elaborate?
    > thanks
    >> An interesting aspect for this group might be that coriolis and rhumb line
    >> corrections were extremely important aspects of bubble sextant operation,
    >> and could reach as high as 28 nm at 450 kts at high latitudes.
    >> Ken Gebhart
    Sorry not to answer right away, but here it is:
    To elaborate on errors from using bubble sextants in airplanes, there are
    actually three to consider.  They are coriolis, rhumb line, and wander
    corrections.  All have to do with accelerations to the sextant bubble caused
    by flying a curved path as seen from space.  The last, wander, is a
    catch-all that has to do with flying into differing air masses, ie. changing
    wind or pressure gradients.  These changes are not apparent to the
    airplane?s occupants, and in my opinion, are rarely allowed for.  The other
    two corrections are substantial, and easy to incorporate into the
    navigator?s analysis.
    To visualize coriolis, consider a plane flying from 50N lat on some
    meridian, to 40N on the same meridian.  If the Earth?s rotation were halted,
    the plane would fly a simple great circle path to its destination.  But let
    the Earth resume its rotation, and the plane would have to make a constant
    slight turn to the east  (as seen from space) to intercept his destination.
    Thus the curved path would deflect his sextant bubble from the true
    vertical.  The math formula for this is Z=2.63? x V x sin L, where Z is the
    deflection of the LOP in minutes of arc to the right of track (in the N
    hemisphere, to the left otherwise), V is ground speed in hundreds of knots,
    and L is latitude.  Looking at the table of this correction which is printed
    in each volume of HO-249 (back cover), it will be seen that this correction
    is 0 at the equator, and moves up to 11 nm at 60 N at 450 kts.
    Rhumb line error occurs when a constant heading is flown which results in a
    curved path over the surface of the Earth as opposed to a great circle path
    which is straight.  Prior to GPS, INS, and GNS navigation systems which
    could engage the autopilot directly to keep cross track error on a great
    circle track to zero, pilots could only set a heading into the autopilot.
    This meant that no matter how often they changed heading (to approximate a
    great circle path), they were always flying rhumb line segments.This error
    is additive to coriolis when flying east, and subtractive when heading west.
    At 60N and flying east or west is is about 5 nm at 450 Kts.  For the math
    majors the formula is Z=0.146? x V squared x sinA x tan L, where A is Track
    in degrees.
    Having said all of the above, I am moved to make some kind of comment.
    Isn't it amazing that there are so many facets to celestial navigation?
    Surely this list has to be the largest repository of learned and odd items
    on the subject in existence.
    Ken Gebhart

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